// CSE 143, Winter 2012
// Each TreeSet object represents a Set storing a collection of unique objects as
// its elements.  This class is based on the SearchTree we wrote in previous lectures.
// A Set does not allow duplicates to be added.
//
// The key differences between SearchTree and TreeSet are:
//  * TreeSet implements a Set interface representing the Set abstract data type (ADT).
//  * TreeSet places its TreeNode as an inner class rather than as a separate file.
//  * TreeSet uses a generic type parameter, <E>, to store any kind of data (not just ints).
//
// class invariant: nodes are always kept in proper BST (left-to-right) sorted order.

import java.util.NoSuchElementException;

public class TreeSet<E extends Comparable<E>> implements Set<E> {
	private TreeNode overallRoot;
	private int size;

	// Constructs an empty set.
	public TreeSet() {
		overallRoot = null;
		size = 0;
	}

	// Adds the given value to this set, if it was not already in the set.
	// If the element is already a member of this set, adding it again has no effect.
	public void add(E value) {
		overallRoot = add(overallRoot, value);
	}

	// private recursive helper for add
	// uses the "x = change(x)" pattern:
	//   pass in current state of root
	//   return out desired new state of root
	private TreeNode add(TreeNode root, E value) {
		if (root == null) {
			root = new TreeNode(value);   // reached dead end; put new node here
			size++;
		} else if (value.compareTo(root.data) > 0) {
			root.right = add(root.right, value);
		} else if (value.compareTo(root.data) < 0) {
			root.left = add(root.left, value);
		} // else a duplicate; do nothing
		return root;
	}

	// Returns true if this set contains the given element value.
	public boolean contains(E value) {
		return contains(overallRoot, value);
	}

	// private recursive helper for contains
	private boolean contains(TreeNode root, E value) {
		if (root == null) {
			return false;
		} else if (value.compareTo(root.data) > 0) {
			return contains(root.right, value);
		} else if (value.compareTo(root.data) < 0) {
			return contains(root.left, value);
		} else {
			// value.equals(root.data); found it!
			return true;
		}
	}

	// Returns the minimum value in this set.
	// Throws a NoSuchElementException if this set is empty.
	public E getMin() {
		if (overallRoot == null) {
			throw new NoSuchElementException("empty tree");
		}
		return getMin(overallRoot);
	}
	
	// private recursive helper for getMin
	private E getMin(TreeNode root) {
		if (root.left == null) {
			return root.data;
		} else {
			return getMin(root.left);
		}
	}
	
	// Returns true if this set does not contain any elements.
	public boolean isEmpty() {
		return size == 0;
	}

	// Prints all elements of this tree in a left-to-right order (in-order) traversal.
	public void print() {
		print(overallRoot);
	}

	// private recursive helper for print
	private void print(TreeNode root) {
		if (root != null) {
			print(root.left);
			System.out.print(root.data + " ");
			print(root.right);
		} // implicit base case: else do nothing
	}
	
	// Removes the given value from this set, if it is found in this set.
	// If the element is not found, calling this method has no effect.
	public void remove(E value) {
		overallRoot = remove(overallRoot, value);
	}
	
	// private recursive helper for remove
	private TreeNode remove(TreeNode root, E value) {
		if (root == null) {
			// nothing here; do nothing?
		} else if (value.compareTo(root.data) < 0) {
			root.left = remove(root.left, value);
		} else if (value.compareTo(root.data) > 0) {
			root.right = remove(root.right, value);
		} else { // (value == root.data)
			// found it! remove now.
			size--;
			if (root.left == null && root.right == null) {
				// leaf
				root = null;
			} else if (root.right == null) {
				// only left child
				root = root.left;
			} else if (root.left == null) {
				// only right child
				root = root.right;
			} else {
				// hard case: two children; replace me with min from my right
				E rightMin = getMin(root.right);
				root.right = remove(root.right, rightMin);
				root.data = rightMin;
			}
		}
		return root;
	}
	
	// Returns the number of elements in this set.
	public int size() {
		return size;
	}
	
	
	// Each TreeNode object stores a single node of a binary tree.
	// The class has just public data fields and constructors.
	// This version of our code places the node as an inner class.
	private class TreeNode {
		public E data;         // data stored at this node
		public TreeNode left;  // reference to left subtree
		public TreeNode right; // reference to right subtree

		// Constructs a leaf node with the given data.
		public TreeNode(E data) {
			this(data, null, null);
		}

		// Constructs a leaf or branch node with the given data and links.
		public TreeNode(E data, TreeNode left, TreeNode right) {
			this.data = data;
			this.left = left;
			this.right = right;
		}
	}
}